In London, George Osborne tried to win over voters undecided over ­independence by ­promising to publish within days a cross-party plan to offer more powers to Edinburgh if Scotland stays in the UK.

This would include handing more tax-raising powers and control over welfare to the Scottish Parliament.

The YouGov found just 54% of ­Scottish voters wanted the Queen as head of state with 31% preferring an elected figurehead.

Across the UK as a whole, only 45% felt she should remain the Scottish head of state if the country votes for independence on 17 October.

A senior source on the Yes campaign said "questions were being asked" over the Queen's apparent bias after she was reportedly disturbed by the prospect of Scotland breaking away from the UK.

He said: "It's very seldom you get any personal opinion from the monarch, that's why we're dubious.

"It's important to realise that retaining the Queen as our monarch after a yes vote is in the white paper.

"If we vote yes, that's the situation that will sustain.

"But we won't actually become independent until 2016 when the first elections will be to the independent parliament."

A palace spokeswoman denied suggestions that the Queen had a bias in the vote, ­stating that she is "strictly neutral".

A spokeswoman said: "The ­referendum is a matter for the people of Scotland – the Queen remains strictly neutral on this, as she does on all political issues.

"The Queen has maintained a close interest in the referendum as she does with all major matters of public debate and is being kept informed by her ­ministers and officials in the usual way."

The Queen and Prince Philip watched the Highland Games in Braemar, Aberdeenshire, over the weekend.

The monarch has previously stated her position on the union. In a speech to MPs on her Silver Jubilee in 1977, she said: "I was crowned Queen of the United Kingdom of Great Britain and Northern Ireland.

"Perhaps the jubilee is the time to remind ourselves of the benefits which union has conferred, at home and in our international dealings, on the inhabitants of all parts of the United Kingdom."